Global stability conditions of a system with hysteresis nonlinearity

Abstract

The paper discusses a two-dimensional automatic control system that contains a single hysteresis element of the general form. Systems of this type are mathematical models of real control systems and have been considered in many papers on this subject. In this paper, a system phase space, which is a manifold with a boundary, is constructed. The conditions under which the system is globally stable in a certain sense are formulated. The term sliding mode is used in the formulation ([15], Fig. 4).